Evaluation method of semiconductor device, manufacturing method of the semiconductor device, design management system of device comprising the semiconductor device, dose amount control program for the semiconductor device, computer-readable recording medium recording the program, and dose amount control apparatus

ABSTRACT

There is provided a new method of obtaining the dopant activation rate of a device accurately and simply in a different way from a method of obtaining a carrier density with use of a Hall measurement or CV measurement, and also provided a production method of a device performed with a proper threshold voltage control, that is, a dose amount control, according to the obtained activation rate. The inventor devised a method in which the activated dopant density (first dopant density) in a semiconductor film is obtained from the threshold voltage and the flat band voltage of a device, then the dopant activation rate is obtained from the ratio of the obtained activated dopant density to the added dopant density (second dopant density) obtained by SIMS analysis. The invention allows easily obtaining the dopant activation rate in the channel region and the impurity region of the device.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a device comprising asemiconductor device, particularly relates to an evaluation method ofthe dopant density and the dopant activation rate in a semiconductorfilm, and provides a design management system (production managementsystem) on which these things are taken into account. Further, theinvention provides a program to make a computer obtain the dopantactivation rate and control the dose amount.

[0003] 2. Description of the Related Art

[0004] In a field effect transistor (hereinafter referred to as a‘FET’), a thin film transistor (hereinafter referred to as a ‘TFT’),which is an example of FETs, and other semiconductor devices, thethreshold voltage is an important parameter that decides the operatingpoint. The threshold voltage is decided by the factors such as theactivation rate of added dopant (impurity), (hereinafter referred to asthe ‘dopant activation rate), and the distribution of carriersconcentration (hereinafter referred to as ‘carrier density’).

[0005] In other words, it is necessary to control the dopant activationrate and the carrier density so that semiconductor devices obtainpredetermined characteristics. The dopant activation rate is representedby the ratio of the amount of dopant which is actually activated to theamount of dopant which is added to a semiconductor film. The carrierdensity is the amount of carriers that actually flow in the channelregion, which also varies depending on the presence of an appliedvoltage. Particularly, when the dopant activation rate is 100%, thedopant density and the carrier density are equal.

[0006] Conventionally, the carrier density is obtained by the Hallmeasurement, the CV measurement (capacitance measurement), or SIMSanalysis.

[0007] As an example using SIMS analysis, which is a measurement of theabove carrier density, there is a method such that: primary ions areemitted onto the surface of a conductive impurity-doped semiconductorfilm under the condition that the surface thereof is charged withelectricity; the strength of the secondary ions having a specific energyemitted from the surface is sequentially measured with the elapse ofemitting time of the primary ions; and, from the concentration ofcarriers corresponding to the strength of the secondary ions and theetching amount of the semiconductor film corresponding to the time ofemitting of the primary ions, the carrier distribution in the depthdirection in the semiconductor film is obtained (refer to JapanesePatent Laid-Open No. H7-66258).

[0008] It is difficult, however, to measure a thin film such as a TFT orSOI membrane by the Hall measurement. This is because, as the film isthinner, the resistance of the film is greater, and the Hall current issmaller, which makes it very difficult to obtain the carrier density.Particularly, in the case of a semiconductor device formed on a glasssubstrate, the CV measurement which requires grounding of the substrateis useless.

[0009] Further, the Hall measurement and the CV measurement require aspecific TEG (Test Element of Groups) for measurement that is differentfrom a device, and the carrier density of a TEG is measured. Since theTEG is produced under conditions different from the thermal history ofthe actual device process, it is possible that the carrier density andthe dopant activation rate are different from those in the device.

[0010] Still further, with an actual device, the dopant densitycontributing to carriers (that is the activated dopant density) changesa lot with the state of the semiconductor film due to the high defectdensity in the film when the semiconductor film is non-crystal orpolycrystal.

[0011] On the other hand, even a carrier density obtained from asinglecrystal wafer having a small defect density is not necessarily thesame as the value of the actual device. This is because even if thedopant activation rate of the TEG is obtained by the Hall measurement,the CV measurement, or SIMS analysis, since the actual device goesthrough several thermal processes before completion, it is highlypossible that the above obtained dopant activation rate is differentfrom that in the semiconductor film of the device.

[0012] Further, to obtain the carrier density with high accuracy usingthe Hall measurement or the CV measurement, it is necessary to measure amaximum possible capacitance (in case of the CV measurement) or amaximum possible Hall current (in case of the Hall measurement).Therefore, the TEG for the Hall measurement or the CV measurement ismuch greater compared to the device. Consequently, since the obtainedcarrier density is an average value in a wide region, the dispersion ofthe values in a microscopic region cannot be evaluated.

SUMMARY OF THE INVENTION

[0013] To solve the problem, the invention provides a new method ofobtaining a dopant activation rate of a device accurately and easily.The invention provides a production method of a device with properthreshold voltage control, that is, control of the dose amount,according to the obtained activation rate.

[0014] The invention also provides a design management system(production management system) to carry out efficient designing ofdevices having desired characteristics by setting the doping amount of adoping system to a proper value.

[0015] Still further, the invention provides a program to obtain a doseamount in a short time with a constant result independently of theexperience of the executor.

[0016] A device means a set of a plurality of semiconductor devices,represented by FET, having a certain function (shift resistors, drivingtransistors, etc.). A set of a plurality of the devices constructs aliquid crystal display apparatus, an EL display apparatus, or anotherdisplay apparatus.

[0017] Taking the above problems into account, the inventor devised amethod of obtaining the dopant activation rate in which the dopantdensity (first dopant density) of activated dopant in a semiconductorfilm is obtained from the threshold voltage and the flat band voltage ofa device, then the dopant activation rate is obtained from the ratio ofthe above obtained dopant density (first dopant density) of theactivated dopant to the added dopant density (second dopant density)that is obtained by SIMS analysis (Secondary Ion Mass Spectrometry).

[0018] Instead of SIMS analysis, physical analysis or chemical analysisby which the added dopant density can be obtained may be applied. Forexample, by peeling the film which is added with dopant and melting itin a solvent, the added dopant density can be obtained from the massratio.

[0019] Specifically, in the invention, the threshold voltage and theflat band voltage are obtained from the Vg-Id (the drain current for thegate voltage) curve of a device. Then, using theoretical formulas by theinvention and the activated dopant density to obtain is defined as avariable, the dopant density is obtained such that the above variableaccords with the difference between the threshold voltage and the flatband voltage obtained from the Vg-Id curve. Thus decided value is theactivated dopant density. Next, in the invention, the dopant activationrate is obtained by dividing the activated dopant density by the addeddopant density which is obtained by SIMS analysis.

[0020] The flat band voltage is defined by the gate voltage at the timewhen the energy band in semiconductor becomes flat in Vg-Idcharacteristics of the device. If the gate voltage is increased from theflat band voltage positively or negatively, then the band goes intoinversion and a current begins to flow. Therefore, the flat band voltagecan be recognized as the inflection between off-current and on-currenton the Vg-Id curve.

[0021] According to the invention, the dopant activation rate can beobtained not only for a semiconductor film, that is, a channel region,but also for the source region, the drain region, the LDD region, andthe like (hereinafter, totally referred to as ‘the impurity region’).For example, the dopant activation rate of the LDD region can beobtained as follows.

[0022] First of all, dopant is implanted into a semiconductor film thesame as into the LDD region. For example, after an insulating film isformed on the semiconductor film, dopant is implanted, then theinsulating film on the semiconductor film is removed by etching,further, the semiconductor film is patterned to become a device of adesired size, and a gate insulating film and a gate electrode are formedon the semiconductor film to produce a semiconductor device.

[0023] Then, from the Vg-Id curve of the produced semiconductor device,the threshold voltage and the flat band voltage are obtained, andthereby the activated dopant density in the LDD region can be obtained.Further, if the activated dopant density is coupled with SIMS analysisdata, the dopant activation rate in the source region or the drainregion can be obtained.

[0024] Also, the dopant activation rate and others obtained fromtheoretical formulas of the invention may be databased. By comparison ofthe dopant activation rate and others with the threshold voltage and theflat band voltage in the channel region or the impurity region of thesemiconductor device constructing the device, information on the addeddopant density can be obtained. In reverse, from the added dopantdensity and the dopant activation rate, the threshold voltage and theflat band voltage can be estimated. By databasing the dopant activationrate and others as such, the dose amount can be set more quicklycompared to known methods in which a predetermined dose amount is setfrom a plurality of samples.

[0025] By the above evaluation method according to the invention, thedopant activation rate in the channel region and the impurity region ofa device can be easily obtained. In other words, according to theinvention, it is possible to use not a TEG for measurement but theactual device. Also, since the dopant activation rate in a region assmall as several micrometers can be obtained, dispersion of the valuesin a microscopic region can be evaluated. Further, the measurementmethod according to the invention allows evaluation on a device with athin film.

[0026] Still further, according to the invention, a device designmanagement system that determines a proper doping amount (dose amount),according to the obtained dopant activation rate, can be achieved. Forexample, a dopant density that maximizes the dopant activation rate canbe obtained, and then the dose amount can be fed back to the dopingsystem. Further, when repairing or starting the doping system, thedopant activation rate can be used to make a fine adjustment of the doseamount.

[0027] Depending on the purpose of evaluation, the dopant activationrate or the activated dopant density may be used. For example, thedopant activation rate can be used for evaluation of the quality of asemiconductor film, and the activated dopant density can be used forobtaining the dose amount. However, since it is possible that time isnot taken into account by merely setting the dose amount, it ispreferable to use the dopant activation rate for efficient doping.

[0028] A device that is formed by controlling the dose amount to be aproper amount, according to the invention, has higher electriccharacteristics compared to devices produced by conventional method.Particularly, by the device design management system according to theinvention, devices in which dispersion of the threshold voltage isreduced can be provided. In other words, the invention allowsmanufacturing of products with the efficiency of mass production.

[0029] Further, the dispersion of the threshold voltage among thesemiconductor devices in the same substrate can be reduced. Although ifthe activation rate is low, the threshold voltage is sensitive to theeffects of the factors (heating process and the like), dispersion of thethreshold voltage can be reduced by controlling the dopant activationrate to be high to a certain degree, thereby reducing the dispersion ofthe threshold voltage described above.

[0030] Still further, a method of the invention can be taken as a systemor a program. The program can be recorded in a computer-readablerecording medium such as a hard disk, a CD-ROM, an optical recordingdevice, or a magnetic storage device.

[0031] Semiconductor devices herein include field effect typetransistors represented by TFTs and FETs, and junction type transistorssuch as bipolar transistors. Junction type transistors require fieldeffect type transistors for measurement.

[0032] As described above, the invention provides an accurate and simpleevaluation method for improving stability and reliability of electriccharacteristics of semiconductor devices. The invention also provides aliquid crystal display apparatus, an EL display apparatus, and otherdisplay apparatuses which are reliable and equipped with devicesaccording to the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0033]FIGS. 1A to 1B are diagrams showing an example of a designmanagement system according to the invention;

[0034]FIGS. 2A to 2B are diagrams showing another example of a designmanagement system according to the invention;

[0035]FIGS. 3A to 3B are diagrams showing an example of a computersystem according to the invention;

[0036]FIGS. 4A to 4B are diagram showing a measurement sample accordingto the invention;

[0037]FIG. 5 is a diagram showing an experimental result according tothe invention;

[0038]FIG. 6 is a diagram showing another experimental result accordingto the invention;

[0039]FIG. 7 is a diagram showing another experimental result accordingto the invention;

[0040]FIG. 8 is a diagram showing another experimental result accordingto the invention;

[0041]FIG. 9 is a diagram showing another experimental result accordingto the invention;

[0042]FIG. 10 is a diagram showing another experimental result accordingto the invention;

[0043]FIG. 11 is a diagram showing another experimental result accordingto the invention; and

[0044]FIG. 12 is a flowchart of a software routine according to theinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0045] Embodiment Mode 1

[0046] In the present embodiment mode, theoretical formulas according tothe invention will be described, taking an example, first, of apartially depleted FET, which is possible in the case that the thicknessof the activated layer is relatively large. Partial depletion means thestate that an activated layer gets depleted only partially even under astrong-inversion condition.

[0047] Vth and Vfb denote the threshold voltage and the flat bandvoltage of an FET, respectively. Further, Cox denoted the capacitance ofthe insulating film of the FET, and Q denotes the electric charge thatis induced in the depletion layer. Still further, Vs denotes the surfacepotential. Then, the following formula is valid.

Vg−Vfb=Q/Cox+Vs  (1)

[0048] Vg denotes, herein, the voltage applied to the gate electrode ofthe FET. From this formula, if Vg=Vth, the following formula is valid.

Vth=Vfb+Q/Cox +Vs  (2)

Q=e·Nd·Wmax  (3)

Vs=(e·Nd·Wmax ²)/(2εO·εSi)=2Vf  (4)

[0049] Nd denotes the activated dopant density, and e denotes theelectron charge. Wmax denotes the width of the depletion layer.Potential Vf is given by the difference between Fermi level Ef in a bulkregion which is off the insulating film boundary surface and theintrinsic Fermi level Ei, and represented by the formula (5).

Vf=(Ef−Ei)/e  (5)

[0050] Further, denoting the intrinsic carrier density by ni, thefollowing formula is valid.

Nd=ni·exp((Ef−Ei)/kT)  (6)

[0051] From formulas (4), (5), and (6), the following formula isobtained.

Vs=(2kT/e)·ln(Nd/ni)=(e·Nd·Wmax ²)/(2εO·εSi)  (7)

[0052] The vacuum permittivity and the relative permittivity of asemiconductor are denoted by ε0 and εSi, respectively. From formula (7),Wmax is represented by the flowing formula.

Wmax=[(4εO·εSi·kT)/(e ² ·Nd)·ln(Nd/ni)]^(1/2)  (8)

[0053] From formulas (2), (3), (7), and (8), the following formula isobtained. $\begin{matrix}\begin{matrix}{{{Vth} - {Vfb}} = {{\left( {e \cdot {{Nd}/{Cox}}} \right) \cdot \left\lbrack {{\left( {4\quad ɛ\quad {O \cdot ɛ}\quad {{Si} \cdot {kT}}} \right)/\left( {e^{2} \cdot {Nd}} \right)} \cdot {\ln \left( {{Nd} \cdot {ni}} \right)}} \right\rbrack^{1/2}} +}} \\{{\left( {2{{kT}/e}} \right) \cdot {\ln \left( {{Nd}/{ni}} \right)}}}\end{matrix} & (9)\end{matrix}$

[0054] From formula (9), it will be understood that the activated dopantdensity Nd can be obtained if values are given to Vth and Vfb. However,formula (9) cannot be solved analytically and is necessary to be solvednumerically. Since Nd and ni are of great values indicated by indexes,calculation will be easier if the formula is modified as the followingformula in numerical calculation to reduce the dimension of thevariables.

Vth−Vfb=(e·ni/Cox)(Nd/ni)·[(4εO·εSi·kT)/(e²·(Nd/ni)·ni)·ln(Nd.ni)]^(1/2)+(2kT/e)·ln(Nd/ni)  (10)

[0055] In actual calculation, Nd/ni is set as a variable, and Nd/ni isobtained such that the left side and the right side of formula (10)become an equal value.

[0056] Next, theoretical formulas, according to the invention, for afully depleted FET, which is valid in the case that the film thicknessof an activated layer is small, will be described. In a fully depletiontype, the width of the depletion layer under an inversion condition isequal to the thickness of the activated layer. Denoting the thickness ofthe activated layer by tSi, the following formula is valid in the caseof a fully depleted FET.

Vth−Vfb=(e·Nd·tSi)/Cox+2Vf=(e·(Nd/ni)·ni·tSi)/Cox+(2kT/e)·ln(Nd/ni)  (11)

[0057] In the above, it is necessary to use different calculationformulas depending on the thickness of the activated layer.Determination as to whether a FET is a partial depletion type or a fullydepletion type can almost be made, using the following formulas, thatare: if

tSi>[(4εO·εSi·Vf)/(e·Nd)]^(1/2)

[0058] is valid, then the FET can be determined to be a partialdepletion type, and if

tSi<[(4εO·εSi·Vf)/(e·Nd)]^(1/2)

[0059] is valid, then the FET can be determined to be a fully depletiontype.

[0060] As described above, from the difference between the thresholdvoltage and the flat band voltage of a semiconductor device, theactivated dopant density (Nd) can be obtained, and from the activateddopant density and the added dopant density, the dopant activation ratecan be obtained. To obtain the activated dopant density on an actualsemiconductor, a correction term is taken into account in the aboveformula in some cases.

[0061] The threshold voltage Vth necessary for calculation can beobtained from the Vg-Id curve of the FET. The drain current in thesaturated region according to a gradual channel approximation is givenby the following formula.

Id=(W/2L)·Cox·uFE·(Vg−Vth)²  (12)

[0062] W and L respectively denote the width and the length of thechannel region. Cox and uFE denote the capacitance of the insulatingfilm and the field effect mobility respectively. From formula (12), itwill be understood that if both sides of formula (12) are squared, thesquare of Id and Vg are in a linear relationship. The intersection ofthe linear line and X axis gives the threshold voltage Vth.

[0063] The above formula, and the threshold voltage (Vth) and the flatband voltage (Vfb) which are obtained from the electric characteristics(Vg-Id curve) of the device, determine the dopant density (Nd). Fromthis dopant density (Nd) and the dopant density (Nc) obtained by SIMSanalysis, the dopant activation rate (Nd/Nc) can be easily obtained.

[0064] Also, dopant activation rates obtained according to theinvention, the heating conditions thereof, and doping conditions may bedatabased to obtain the dopant density (Nc) for a measurement samplewhose threshold voltage and flat band voltage have been obtained.

[0065] Further, for a measurement sample whose dopant density (Nc) hasbeen obtained, the threshold voltage and the flat band voltage of a FETproduced according to the measured sample can be obtained on conditionthat heating conditions and doping conditions of respective measurementsamples are the same.

[0066] Although in the present embodiment, an example has been describedusing a FET, the invention can be applied to any device, a TFT forexample, for which the theoretical formulas according to the inventionare valid.

[0067] Embodiment Mode 2

[0068] In the present embodiment mode, a design management system thatfeeds back a dopant activation rate obtained as in the embodiment mode 1to a process of producing devices will be described with reference toFIGS. 1A and 1B.

[0069]FIGS. 1A and 1B are a construction diagram of the designmanagement system and a flowchart thereof, respectively.

[0070] First of all, a semiconductor device to be a device is produced,and then, this device is measured as a measurement sample 101 by a Vg-Idcharacteristics measurement instrument 102 and a SIMS analysis apparatus103. Then, a threshold voltage (Vth) and a flat band voltage (Vfb) whichare obtained from Vg-Id characteristics are input to a computer 105, andthe dopant density (Nd) is computed according to theoretical formulasaccording to the invention. Further, from a dopant density (Nc) obtainedby SIMS analysis and the dopant density (Nd) obtained by the theoreticalformulas, a dopant activation rate is computed by the computer 105.

[0071] Next, according to the obtained dopant activation rate, anoptimum dose amount (for example, a dose amount with the highestactivation rate) in which the threshold voltage is taken into account isdetermined, and a doping system 106 is controlled such that the doseamount is to be the determined amount. In other words, the dopantactivation rate is fed back to the dose amount of the doping system.

[0072] Further, a device simulator may be provided between the computer105 and the doping system 106. For calculation of the device sizenecessary for a circuit, the device simulator requires input of thedopant density (Nd) in the channel region, the source region, or thedrain region. The dopant density (Nd) can be obtained from the thresholdvoltage and the flat band voltage. The dopant density in a LDD sectionwhich is necessary for improving the reliability of the device iscalculated by the device simulator, a dose amount which sets the dopantdensity to a desired value is searched by a personal computer fordatabase, and the obtained dose amount is transmitted to the dopingsystem, thereby making it possible to efficiently produce a reliabledevice.

[0073] The design management system in the present embodiment mode canbe implemented, using the dopant activation rate in either the channelregion or the impurity region.

[0074] As described above, by determining the dose amount from thedopant activation rate, it is possible to efficiently produce a devicewhich is controlled for an optimum threshold voltage.

[0075] Embodiment Mode 3

[0076] In the present embodiment mode, differently from the embodimentmode 2, a design management system in the case of stored dopantactivation rates as a database will be described with reference to FIGS.2A and 2B.

[0077]FIG. 2A is a construction diagram of the design management system,and FIG. 2B is a flowchart of the design management system. The presentembodiment mode can be divided into two routes (i) and (ii) depending onwhich of Vg-Id characteristics measurement and SIMS analysis has beencarried out for a measurement sample.

[0078] First, the route (i) will be described. First, measurement iscarried out on a measurement sample A 201 comprising a semiconductordevice, using a Vg-Id characteristics measuring instrument 202. Then, acomputer 205 computes the doping density (Nd) from the obtainedthreshold voltage and the obtained flat band voltage. Further, storeddopant activation rates and the doping density (Nd) are compared by thecomputer 205. As a result, the dopant density (Nc) of the measurementsample A 201 is obtained.

[0079] According to the obtained dopant density (Nc) and the dopantactivation rate then, the dose amount of a doping system is controlled.In other words, the doping density (Nc) is fed back to the dose amountof the doping system.

[0080] The route (ii) is for the case of performing measurement on ameasurement sample B211 comprising a semiconductor device, using a SIMSanalyzing apparatus 203. The dopant density (Nc) obtained by SIMSanalysis and the stored dopant activation rates are compared by thecomputer 205. As a result, the dopant density (Nd) of the measurementsample B211, and the threshold voltage or the flat band voltage areobtained.

[0081] According to the obtained dopant density (Nd) and the dopantactivation rate then, the dose amount of the doping system iscontrolled. In other words, the threshold voltage and the flat bandvoltage are fed back to the dose amount of the doping system.

[0082] A device simulator may be provided between the computer 205 andthe doping system 206 as well as in the embodiment mode 1.

[0083] As described above, with respect to a plurality of semiconductordevices, the threshold voltage, the flat band voltage, the dopantdensities (Nd, Nc), and the dopant activation rate can be databased. Asa result, an optimum dose amount can be determined by performing eitherVg-Id characteristic measurement or SIMS analysis on the semiconductordevices.

[0084] Embodiment Mode 4

[0085] In the present embodiment mode, a computer system for controllingthe dose amount will be described with reference to FIGS. 3A and 3B.

[0086] Various types of computers including personal computers,workstations, and mainframe computers can be used as a computer of thecomputer system described above. The computer is provided with hardwaredevices, which are equipped on common computers, such as a centralprocessing unit (CPU), a main memory unit (RAM), a coprocessor, an imageaccelerator, a cash memory, an input-output control device (I/O), andthe like. Further, an external storage device such as a hard diskdevice, and communication means such as the Internet may also beprovided.

[0087]FIG. 3A shows a construction diagram of the computer systemcomprising a terminal 301, a doping system 302, a computer 311, and ameasuring instruments 321.

[0088] The terminal 301 comprises a instrument to input productionconditions of semiconductor devices, design conditions of devices, andthe like. As the terminal 301, a personal digital assistant (PDA), acomputer, or the like can be used. The terminal 301 and the dopingsystem 302 are provided at a place (a clean room, for example) toproduce devices.

[0089] The computer 311 comprises a apparatus (computing apparatus 312)for computing the dose amount from the threshold voltage (Vth), the flatband voltage (Vfb), and the dopant density (Nc) that are input from ameasuring instrument 321, and a device (setting device 315) for settingthe dose amount obtained from the computing apparatus to doping system.The computer 311 comprises an output apparatus that allows to output ofthe dose amount by printing or displaying.

[0090] The computer 311 also may comprise a storage apparatus 313 forrecording respective threshold voltages (Vth), flat band voltages (Vfb),dopant densities (Nc), which are obtained from the computing apparatus312, production conditions of semiconductor devices, design conditionsof devices, and the like.

[0091] Further, the computer 311 may comprise a determining apparatus314 for selecting a proper dose amount from the storage instrument 313,according to the production conditions of semiconductor devices, thedesign conditions of devices, and the like. More preferably, conditionsunique to each doping system are stored in the storage instrument 313 sothat a best dose amount can be selected by the determining apparatus314.

[0092] The computer 311 may be installed at a place to produce devicesor a different place. In case of installing the computer 311 at thedifferent place, each condition which is input at the terminal 301 maybe input to the determining apparatus 314 through a network.

[0093] The measuring instrument 321 measures Vg-Id characteristics,which are the electric characteristics of a device, and obtains thethreshold voltage (Vth) and the flat band voltage (Vfb). Further, SIMSanalysis measurement is carried out to obtain the dopant density (Nc) ofthe device. The measuring instrument 321 may be installed at the placeto produce devices or a different place. In case of installing themeasuring device 321 at the different place, each result by themeasuring device may be input to the computing instrument 321 throughthe network. The measuring device 321 and the computer 311 may beinstalled at the same place.

[0094] Next, the two routes of the system will be described, using FIG.3B. Through the route (i), information flows into the doping system, andthrough the route (ii), information selected from the storage instrument313 by the determining apparatus 314 flows into the doping system.

[0095] On the route (i), the dopant density (Nd) is obtained from thethreshold voltage (Vt) and the flat band voltage (Vfb) of the devicewhich are input to the computing apparatus 312. From the dopant density(Nc), the dopant activation rate is derived from the storage instrument.Further, from the dopant activation rate, the dose amount is derivedfrom that. Then, the dose amount is set by the setting apparatus 315,and the dose amount is output to the doping system.

[0096] On the route (ii), from the database stored in the storageinstrument 313, a dopant activation rate that fits the productionconditions of the semiconductor device and the design conditions of thedevice is selected by the determining apparatus 314, and the dopantdensity (Nc) is determined.

[0097] Further, the dose amount for obtaining a predetermined dopantdensity sometimes changes with each doping system. In this case,conditions peculiar to each doping system that are stored in the storageinstrument 313 are referred to, and thus an optimum dose amount forobtaining the above determined dopant density is determined and outputto the doping system.

[0098] Next, as an example of a routine flow of a dose amount controlprogram, the routine described above with (ii) in FIG. 3B will be nowdescribed with reference to FIG. 12.

[0099] First, Vth and Vfb which are obtained from the electriccharacteristics of the measured semiconductor device are input tocalculate the doping density (Nd) from theoretical formulas according tothe invention. Also, the design conditions (the portion to be formed,the construction of the semiconductor device, and the like) of devicesand the production conditions (activation conditions of thesemiconductor film, etc.) of the semiconductor device are input. Then,an optimum dopant activation rate for the design conditions of thedevice is computed, taking the dopant density (Nd) and the productionconditions of the semiconductor device into account. At this time, thedesign conditions of devices, the production conditions of semiconductordevices, and the conditions of the dopant activation rates, which arestored in the database, are referred to, and thus the optimum dopantactivation rate is determined.

[0100] Next, according to the dopant activation rate, the added dopantdensity (Nc) is computed. The doping system needs to be stable enough tobe able to add a certain dose amount, and conditions that enable eachdoping system to add a predetermined dose amount may be databased. Thatis, the database in which the conditions of each doping system arestored is referred to, and thus the dose amount for obtaining thepredetermined dopant density is determined.

[0101] The result of the obtained dose amount is displayed. Then, thedose amount may be output to the doping system, printed out, or outputin another way. Further, data including the obtained dose amount issaved and stored in the database.

[0102] By the computer system, as described above, for controlling thedose amount, the dose amount can be efficiently determined. Further,independently of the experience of the executor, the dose amount can beobtained in a short time with a constant result.

[0103] Embodiment 1

[0104] In the present embodiment, a result of obtaining the dopantactivation rate in the channel region of a device will be described.Boron (B) is used as the dopant.

[0105] First of all, a cross-section (A) of a measurement sample and across-section (B) of a sample for SIMS analysis will be described withreference to FIGS. 4A and 4B.

[0106] As shown in (i) in FIG. 4A, a semiconductor film 401 is formed onan insulating substrate 400. The semiconductor film 401 islaser-crystallized, heat-crystallized, or crystallized using a method ofcrystallizing in which a metallic element that promotes crystallizationis added. In the present embodiment, the semiconductor film iscrystallized by heating.

[0107] As shown in (ii) in FIG. 4A, boron is doped into the crystallizedsemiconductor film 401. At this time, the dose amount is set in sixconditions to form measurement samples 1 to 6 as shown in Table 1. TABLE1 sample number dose amount of boron (/cm²) 1 3.1 × 10¹³   2 5 × 10¹³ 38 × 10¹³ 4 1.3 × 10¹⁴   5 2 × 10¹⁴ 6 3.2 × 10¹⁴  

[0108] For the SIMS sample, after crystallization of the semiconductorfilm, boron is doped under conditions of 1×10¹³/cm², 30 kV, and 5Wwithout being patterned. Thus, the SIMS sample is completed.

[0109] Next, as shown in (iii) in FIG. 4A, the semiconductor film ofonly the measurement sample is patterned into a desired shape, and thedimensions are set to L/W=8/8 μm. Then, the semiconductor films of themeasurement sample and the SIMS sample are covered by forming aninsulating film 402.

[0110] Further, as shown in (iv) in FIG. 4A, a gate electrode is formedby laminating a first conductive film 403 and a second conductive film404. Then, phosphorus (P) is added, with the gate electrode as a mask,and a source and drain region 405, a first low concentration impurityregion 406, and a second low concentration impurity region 407superimposing with the gate electrode are formed, thereby completing ann-channel type TFT.

[0111] Each sample 1 to 6 of the device and the SIMS sample may beformed on the same substrate or on different substrates. In case offorming the SIMS sample on a different substrate, a Si wafer may beused. If the doping system is stable, the SIMS sample may be producedand carry out SIMS analysis in advance. In other words, if implantconditions (GI film thickness, implant energy, etc.) are not changed foreach substrate or each a Lot, it is not necessary to carry out SIMSanalysis for each substrate or a Lot.

[0112] Further, Vg-Id characteristics of the samples 1 to 6 is measured.The result is shown in FIG. 9. The threshold voltages Vth (V) and theflat band voltages of the samples 1 to 6 are obtained from FIG. 9. Theresult is shown in Table 2. TABLE 2 sample number Vth (V) Vfb (V) 1 1.59−0.676 2 1.74 −0.643 3 2.6  −0.162 4 4.26 0.36 5 7.35 0.545 6 8.62 0.714

[0113] From the result, the relationship between the boron dose amountand the threshold voltage is shown in FIG. 5. It will be understood fromFIG. 5 that as the boron dose amount increases, the threshold voltagerises. FIG. 5 shows, however, the relationship between the boron doseamount and the threshold voltage, but does not show the relationshipbetween the activated boron concentration and the threshold voltage.

[0114] Next, the result of SIMS analysis for depth distribution of boronconcentration in the SIMS sample is shown in FIG. 6. In the presentembodiment, as the SIMS sample, a Si wafer formed with an insulatingfilm 1 μm thereon is used, wherein the Si wafer is a different substratefrom the measurement samples. Since the film thickness of thesemiconductor film (Si film) of the SIMS sample is 50 nm, the borondensity can be estimated as approximately 4×10¹⁸/cm³. Also, it can beassumed that the dose amount and the boron concentration obtained fromSIMS are linearly proportional to each other. Therefore, boronconcentrations, other than for the dose amount of 1×10¹³/cm², can besimply estimated from the result in FIG. 6. For example, theconcentration of boron which is present in the semiconductor film whendoping in a dope amount of 5.0×10¹³/cm² is calculated as(5.0×10¹³/1.0×10¹³)×4×10¹⁸/cm³.

[0115] Further, Table 3 shows, the results of the dopant density Ndobtained such that the threshold voltage and the flat band voltageobtained from the Vg-Id curve are given to the theoretical formula, thedopant density Nc obtained from SIMS analysis, and the dopant activationrate (Nd/Nc). TABLE 3 sample number Nd[calculation](/cm³) Nc[SIMS](/cm³)activation rate (%) 1 9.76 × 10¹⁵ 1.24 × 10¹⁹ 0.0787 2 1.11 × 10¹⁶ 2.00× 10¹⁹ 0.0555 3 1.60 × 10¹⁶ 3.20 × 10¹⁹ 0.05 4 3.61 × 10¹⁶ 5.20 × 10¹⁹0.0694 5 1.22 × 10¹⁷ 8.00 × 10¹⁹ 0.153 6 1.67 × 10¹⁷ 1.28 × 10²⁰ 0.13

[0116] From Table 3, the relationship between the dose amount and theactivated dopant density (Nd) is shown in FIG. 7. It will be understoodfrom FIG. 7 that the relationship between the dose amount and theactivated dopant density is not linear. This shows that the dopantactivation rate changes with the dose amount.

[0117] Further, FIG. 8 shows the relationship between the dose amountand the dopant activation rate. It will be understood from FIG. 8 thatthe dose amount and the dopant activation rate are not linearlyproportional. Also, regions where if the dose amount is increased, theactivation rate is reduced can be seen.

[0118] In general, the higher the defect density in the film, the lowerthe activation rate. Therefore, it can be understood that since the rateof the introduced defect for the dose amount becomes higher in someregion, the activation rate drops. If the dose amount is increased more,it can be understood that the activation rate rises because the effectby the high added dopant density is greater than the effect by theintroduced defect density.

[0119] In such a manner, a relative comparison between the defectdensity in the semiconductor films from the dopant activation rate andis possible.

[0120] As described above, since there is no special relationshipbetween the dose amount and the dopant activation rate, it is necessaryto obtain the dopant activation rate for each change of the dose amountor the process, and control the threshold voltage. As described in theembodiment mode, it is also possible to estimate the threshold voltageand the flat band voltage from the dopant activation rate, and estimatethe added impurity amount which is obtained from SISM analysis.

[0121] The invention can be applied to FETs in any structure, forexample, Single drain structures, Gold structures, LDD structures, DualGate structures, and Double Gate structures.

[0122] As the gate insulating film, a monolayer film such as a thermaloxide film, a TEOS film, a SiON film, a nitride film or a multi-layerfilm by a combination thereof can be used. As the gate electrode, amonolayer film of Poly-Si, tungsten, aluminum, titan, tantalum, or thelike, or a multi-layer film by a combination thereof can be used.

[0123] As a substrate to form the semiconductor film, a semiconductorwafer, glass, or quartz can be used. Any of single crystalline,polycrystalline, and amorphous can be applied to the semiconductor film.To the material of the semiconductor film, an element such as Si or Ge,or a compound semiconductor such as GaAs, InP, SiC, ZnSe, or GaN can beapplied. Further, a mixed crystalline semiconductor such as SiGe, orAlxGaAs₁-x can also be applied.

[0124] Further, the invention can be applied to any dopant that acts asan n-type or p-type donor (Phosphorus, Arsenide, Sb), or an n-type orp-type acceptor (Boron, Sn, Al, etc.). Although in the embodiment, theactivation rate of boron, which is a p-type dopant, is obtained using aN type TFT, the activation rate of an n-type dopant can also be obtainedusing an P type FET. For example, if an n-type dopant which acts as adonor is implanted into the active layer, and the threshold voltage andthe flat band voltage are obtained from the Vg-Id curve of a p-type FET,the activation rate of the n-type dopant can be obtained as well.

[0125] Embodiment 2

[0126] In the present embodiment, for measurement samples 1 to 5, thereis shown a result of an in-plane distribution of the threshold voltage(Vth), the flat band voltage (Vfb), and the dopant density (Nd) which isobtained from theoretical formulas according to the invention.

[0127] The in-plane distribution shows a dispersion of the thresholdvoltage (Vth), the flat band voltage (Vfb), and the dopant density (Nd)in the same substrate. First of all, numbers (1,1), (1,2), . . . aregiven to the devices formed on the same substrate. The dispersion of thedevices of the respective numbers is obtained.

[0128]FIG. 10 shows the result with the sample 1, and FIG. 11 shows theresult with the sample 5. X axis and Y axis represent the numbers ((0,0)to (9,9)) given to the devices in a sample, and the devices are providedin a quantity of 10×10.

[0129] As described above, according to the invention, even thedispersion of the dopant density in a microscopic region in amicroscopic region in a substrate can be evaluated, which is notpossible by known methods.

[0130] By the new evaluation method of semiconductor devices accordingto the invention, the dopant activation rate of a device can easily beobtained. The invention provides a method of producing a device which isperformed with proper threshold voltage control, that is, dose amountcontrol according to the obtained dopant activation rate.

[0131] Further, the invention provides a design management system of adevice for efficiently designing a device having desired characteristicsby setting the doping amount of a doping system to a proper value.

[0132] Still further, the invention provides a program or acomputer-readable medium by which a dose amount of a certain result canbe obtained in a short time, independently of the experience of theexecutor.

What is claimed is:
 1. An evaluation method of a semiconductor devicecomprising: measuring a drain current characteristics of a gate voltageof the semiconductor device; obtaining a threshold voltage and a flatband voltage from a drain current characteristics of a gate voltage ofthe semiconductor device; obtaining an activated dopant density from thethreshold voltage and the flat band voltage; and obtaining an addeddopant density in the semiconductor device.
 2. The evaluation method ofthe semiconductor device according to claim 1, wherein the added dopantdensity in the semiconductor device is obtained by secondary ion massspectrometry analysis.
 3. The evaluation method of the semiconductordevice according to claim 1, wherein the activated dopant density andthe added dopant density in a channel region of the semiconductor deviceare obtained.
 4. The evaluation method of the semiconductor deviceaccording to claim 1, wherein the activated dopant density and the addeddopant density in an impurity region of the semiconductor device areobtained.
 5. The evaluation method of the semiconductor device accordingto claim 1, further comprising obtaining a dopant activation rate fromthe activated dopant density and the added dopant density.
 6. A devicedesign management system comprising: a means for measuring drain currentcharacteristics of a gate voltage of a semiconductor device constructinga device; a computer having a means for computing an activated dopantdensity from the drain current characteristics of the gate voltage; anda means for measuring an added dopant density in the semiconductordevice, wherein the computer has a function which computes a dopantactivation rate from the activated dopant density and the added dopantdensity, and determines a dose amount from the dopant activation rate.7. A device design management system comprising: a means for measuringdrain current characteristics of a gate voltage of a semiconductordevice constructing a device, and obtaining a threshold voltage and aflat band voltage; and a computer having a means for computing anactivated dopant density from the threshold voltage and the flat bandvoltage, and a dopant activation rate, wherein the computer has afunction to determine a dose amount from the dopant activation rate andthe activated dopant density.
 8. A device design management systemcomprising: a means for measuring an added dopant density in asemiconductor device constructing a device; and a computer having ameans for computing a threshold voltage and a flat band voltage from thedopant density and a dopant activation rate, wherein the computer has afunction to determine a dose amount from the dopant activation rate, andthe threshold voltage and the flat band voltage.
 9. A production methodof a semiconductor device comprising: forming a semiconductor film on aninsulating surface; crystallizing the semiconductor film; adding dopantto the crystallized semiconductor film at a dose amount, wherein thedose amount of the dopant is determined in accordance with a dopantactivation rate of the dopant in a channel region of the semiconductorfilm; and activating the added dopant in the semiconductor film.
 10. Aproduction method of a semiconductor device comprising: forming asemiconductor film on an insulating surface; crystallizing thesemiconductor film; adding dopant to the crystallized semiconductor filmat a dose amount to form a source region and a drain region, wherein thedose amount of the dopant is determined in accordance with a dopantactivation rate of the dopant; and activating the added dopant insemiconductor film.
 11. A dose amount control program for a computerthat controls a dose amount in a semiconductor device, said computercomprising: a computing means for computing a dopant activation ratefrom a threshold voltage and a flat band voltage of the semiconductordevice; and a setting means for setting a predetermined dose amountaccording to the dopant activation rate obtained from the computingmeans.
 12. The dose amount control program according to claim 11,wherein the computing means obtains an activated dopant density by aformulaVth − Vfb = (e ⋅ ni/Cox)(Nd/ni) ⋅ [(4  ɛ  O ⋅ ɛ  Si ⋅ kT)/(e² ⋅ (Nd/ni) ⋅ ni) ⋅ ln (Nd ⋅ ni)]^(1/2) + (2kT/e) ⋅ ln (Nd/ni)

(herein, Vth: threshold voltage, Vfb: flat band voltage, e: electroncharge, ni: intrinsic carrier density, Cox: semiconductor deviceinsulating film capacitance, Nd: activated dopant density, ε0: vacuumdielectric constant, εSi: semiconductor dielectric constant, k:Boltzmann constant, T: absolute temperature), and obtains a dopantactivation rate from the activated dopant density and an added dopantdensity.
 13. The dose amount control program according to claim 11,wherein the computing means obtains an activated dopant density by aformula Vth−Vfb =(e·(Nd/ni)·ni·tSi)/Cox+(2kT/e)·ln(Nd/ni) (herein, Vth:threshold voltage, Vfb: flat band voltage, e: electron charge, ni:intrinsic carrier density, tSi: active layer thickness, Cox:semiconductor device insulating film capacitance, Nd: activated dopantdensity, k: Boltzmann constant, T: absolute temperature), and obtains adopant activation rate from the activated dopant density and an addeddopant density.
 14. A dose amount control program for a computer thatcontrols a dose amount in a semiconductor device, said computercomprising: a computing means for computing a dopant activation ratefrom a threshold voltage and a flat band voltage of the semiconductordevice; a storage means for recording dopant activation rates that areobtained by the computing means with respect to a plurality ofsemiconductor devices with different production conditions; adetermining means for selecting a dopant activation rate of apredetermined semiconductor device from the storage means; and a settingmeans for setting a dose amount, according to the dopant activation rateselected by the determining means.
 15. The dose amount control programaccording to claim 14, wherein the computing means obtains an activateddopant density by a formulaVth − Vfb = (e ⋅ ni/Cox)(Nd/ni) ⋅ [(4  ɛ  O ⋅ ɛ  Si ⋅ kT)/(e² ⋅ (Nd/ni) ⋅ ni) ⋅ ln (Nd ⋅ ni)]^(1/2) + (2kT/e) ⋅ ln (Nd/ni)

(herein, Vth: threshold voltage, Vfb: flat band voltage, e: electroncharge, ni: intrinsic carrier density, Cox: semiconductor deviceinsulating film capacitance, Nd: activated dopant density, ε0: vacuumdielectric constant, εSi: semiconductor dielectric constant, k:Boltzmann constant, T: absolute temperature), and obtains a dopantactivation rate from the activated dopant density and an added dopantdensity.
 16. The dose amount control program according to claim 14,wherein the computing means obtains an activated dopant density by aformula Vth−Vfb=(e·(Nd/ni)·ni·tSi)/Cox+(2kT/e)·ln(Nd/ni) (herein, Vth:threshold voltage, Vfb: flat band voltage, e: electron charge, ni:intrinsic carrier density, tSi: active layer thickness, Cox:semiconductor device insulating film capacitance, Nd: activated dopantdensity, k: Boltzmann constant, T: absolute temperature), and obtains adopant activation rate from the activated dopant density and an addeddopant density.
 17. A computer-readable recording medium that records adose amount control program for a computer that controls a dose amountin a semiconductor device, said computer comprising: a computing meansfor computing a dopant activation rate from a threshold voltage and aflat band voltage of the semiconductor device; a setting means forsetting a predetermined dose amount according to the dopant activationrate obtained from the computing means; and a means for outputting thedose amount that is set by the setting means.
 18. The computer-readablerecording medium according to claim 17 that records a dose amountcontrol program, wherein the computing means obtains an activated dopantdensity from a formulaVth − Vfb = (e ⋅ ni/Cox)(Nd/ni) ⋅ [(4  ɛ  O ⋅ ɛ  Si ⋅ kT)/(e² ⋅ (Nd/ni) ⋅ ni) ⋅ ln (Nd ⋅ ni)]^(1/2) + (2kT/e) ⋅ ln (Nd/ni)

(herein, Vth: threshold voltage, Vfb: flat band voltage, e: electroncharge, ni: intrinsic carrier density, Cox: semiconductor deviceinsulating film capacitance, Nd: activated dopant density, ε0: vacuumdielectric constant, εSi: semiconductor dielectric constant, k:Boltzmann constant, T: absolute temperature), and obtains a dopantactivation rate from the activated dopant density and an added dopantdensity.
 19. The computer-readable recording medium according to claim17 that records a dose amount control program, wherein the computingmeans obtains an activated dopant density from a formulaVth−Vfb=(e·(Nd/ni)·ni·tSi)/Cox+(2kT/e)·ln(Nd/ni) (herein, Vth: thresholdvoltage, Vfb: flat band voltage, e: electron charge, ni: intrinsiccarrier density, tSi: active layer thickness, Cox: semiconductor deviceinsulating film capacitance, Nd: activated dopant density, k: Boltzmannconstant, T: absolute temperature), and obtains a dopant activation ratefrom the activated dopant density and an added dopant density.
 20. Acomputer-readable recording medium that records a dose amount controlprogram for a computer that controls a dose amount in a semiconductordevice, said computer comprising: a computing means for computing adopant activation rate from a threshold voltage and a flat band voltageof the semiconductor device; a storage means for recording dopantactivation rates that are obtained by the computing means with respectto a plurality of semiconductor devices with different productionconditions; a determining means for selecting a dopant activation rateof a predetermined semiconductor device from the storage means; and asetting means for setting a dose amount according to the dopantactivation rate selected by the determining means.
 21. Thecomputer-readable recording medium according to claim 20 that records adose amount control program, wherein the computing means obtains anactivated dopant density from a formulaVth − Vfb = (e ⋅ ni/Cox)(Nd/ni) ⋅ [(4  ɛ  O ⋅ ɛ  Si ⋅ kT)/(e² ⋅ (Nd/ni) ⋅ ni) ⋅ ln (Nd ⋅ ni)]^(1/2) + (2kT/e) ⋅ ln (Nd/ni)

(herein, Vth: threshold voltage, Vfb: flat band voltage, e: electroncharge, ni: intrinsic carrier density, Cox: semiconductor deviceinsulating film capacitance, Nd: activated dopant density, α0: vacuumdielectric constant, εSi: semiconductor dielectric constant, k:Boltzmann constant, T: absolute temperature), and obtains a dopantactivation rate from the activated dopant density and an added dopantdensity.
 22. The computer-readable recording medium according to claim20 that records a dose amount control program, wherein the computingmeans obtains an activated dopant density from a formulaVth−Vfb=(e·(Nd/ni)·ni·tSi)/Cox+(2kT/e)·ln(Nd/ni) (herein, Vth: thresholdvoltage, Vfb: flat band voltage, e: electron charge, ni: intrinsiccarrier density, tSi: active layer thickness, Cox: semiconductor deviceinsulating film capacitance, Nd: activated dopant density, k: Boltzmannconstant, T: absolute temperature), and obtains a dopant activation ratefrom the activated dopant density and an added dopant density.
 23. Adose amount control device for a semiconductor device, comprising: ameans for inputting a threshold voltage and a flat band voltage of thesemiconductor device, or a dopant density therein; a computing means forcomputing a dopant activation rate from the threshold voltage and theflat band voltage; a setting means for setting a predetermined doseamount according to the dopant activation rate obtained from thecomputing means; and a means for outputting the dose amount that is setby the setting means.
 24. The dose amount control device according toclaim 23, wherein the computing means obtains an activated dopantdensity from a formulaVth − Vfb = (e ⋅ ni/Cox)(Nd/ni) ⋅ [(4  ɛ  O ⋅ ɛ  Si ⋅ kT)/(e² ⋅ (Nd/ni) ⋅ ni) ⋅ ln (Nd ⋅ ni)]^(1/2) + (2kT/e) ⋅ ln (Nd/ni)

(herein, Vth: threshold voltage, Vfb: flat band voltage, e: electroncharge, ni: intrinsic carrier density, Cox: semiconductor deviceinsulating film capacitance, Nd: activated dopant density, ε0: vacuumdielectric constant, εSi: semiconductor dielectric constant, k:Boltzmann constant, T: absolute temperature), and obtains a dopantactivation rate from the activated dopant density and an added dopantdensity.
 25. The dose amount control device according to claim 23,wherein the computing means obtains an activated dopant density from aformula Vth−Vfb=(e·(Nd/ni)·ni·tSi)/Cox+(2kT/e)·ln(Nd/ni) (herein, Vth:threshold voltage, Vfb: flat band voltage, e: electron charge, ni:intrinsic carrier density, tSi: active layer thickness, Cox:semiconductor device insulating film capacitance, Nd: activated dopantdensity, k: Boltzmann constant, T: absolute temperature), and obtains adopant activation rate from the activated dopant density and an addeddopant density.
 26. A dose amount control device for a semiconductordevice, comprising: a means for inputting production conditions of thesemiconductor device or design conditions of a device including thesemiconductor device; a computing means for computing a dopantactivation rate from a threshold voltage and a flat band voltage of asemiconductor device to be measured; a storage means for recordingdopant activation rates that are obtained by the computing means withrespect to a plurality of semiconductor devices with differentproduction conditions; a determining means for selecting a dopantactivation rate of a predetermined semiconductor device from the storagemeans; a setting means for setting a dose amount according to the dopantactivation rate selected from the determining means; and a means foroutputting a dose amount that is set by the setting means.
 27. The doseamount control device according to claim 26, wherein the computing meansobtains an activated dopant density from a formulaVth − Vfb = (e ⋅ ni/Cox)(Nd/ni) ⋅ [(4  ɛ  O ⋅ ɛ  Si ⋅ kT)/(e² ⋅ (Nd/ni) ⋅ ni) ⋅ ln (Nd ⋅ ni)]^(1/2) + (2kT/e) ⋅ ln (Nd/ni)

(herein, Vth: threshold voltage, Vfb: flat band voltage, e: electroncharge, ni: intrinsic carrier density, Cox: semiconductor deviceinsulating film capacitance, Nd: activated dopant density, ε0: vacuumdielectric constant, εSi: semiconductor dielectric constant, k:Boltzmann constant, T: absolute temperature), and obtains a dopantactivation rate from the activated dopant density and an added dopantdensity.
 28. The dose amount control device according to claim 26,wherein the computing means obtains an activated dopant density from aformula Vth−Vfb=(e·(Nd/ni)·ni·tSi)/Cox+(2kT/e)·ln(Nd/ni) (herein, Vth:threshold voltage, Vfb: flat band voltage, e: electron charge, ni:intrinsic carrier density, tSi: active layer thickness, Cox:semiconductor device insulating film capacitance, Nd: activated dopantdensity, k: Boltzmann constant, T: absolute temperature), and obtains adopant activation rate from the activated dopant density and an addeddopant density.
 29. An evaluation method of a semiconductor devicecomprising: measuring a drain current characteristics of a gate voltageof the semiconductor device; obtaining an activated dopant density fromthe drain current characteristics of the gate voltage of thesemiconductor device; obtaining an added dopant density in thesemiconductor device; and obtaining a dopant activation rate from theactivated dopant density and the added dopant density.